Optimization by Pontryagin's maximum principle on the analog computer

✍ Scribed by E. Stanley Lee

• Publisher: American Institute of Chemical Engineers
• Year: 1964
• Tongue: English
• Weight: 738 KB
• Volume: 10
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690100308

✦ Synopsis

A computational method has been developed for obtaining the solution to a class of optimization problems by the combined use of the maximum principle and a maximum (or minimum) seeking technique on the analogue computer. Various maximum seeking techniques can be used for this method. However i f the random search technique is used, this computational method has the advantage of being able to investigate a farge number of operating (or controlling) variables.

The calculation procedure is essentially a trial-and-error procedure which is alternately integration and maximum seeking operations. The variables over which the system is to be optimized are approximated by a finite number of straight line segments n. Thus the maximum (or minimum) of the Hamiltonian function which is obtained by the maximum principle need only be obtained a t n + 1 points along the optimization path (or trajectory).

To illustrate the use of the method the optimum operating variable profiles (or gradients) in a tubular chemical reactor were computed.

The present method, in addition to making it easier to investigate systems with a moderate number of state variables, can be used to solve problems with almost any kind of constraints ond performance index encountered in ordinary optimum design problems. I t offers some possibilities for on-line optimizing control of a process. A special purpose analogue computer could be built for this use.